Archive for December, 2011

He needs both hands to count up to seven.
And I wish him to Hell, not to Heaven.
He’s called Bruce, he wears ugg,
He’s a lout, he’s a thug,
And his surname must surely be Bevan.

Apart from being an uncommon surname, in Queensland, Australia, a bevan denotes an unsophisticated male from the wrong social class or part of town. In other parts of the country he is known as a bogan. Ugg is thick sheepskin used for bevans’ boots. Other signs of “bevanism” include panel vans, flannel shirts and obnoxious hard-rock music.

May the sun shine on you, Michael, and may your socks fit perfectly today. Not so loose that they bunch at your ankles, yet not so tight that they cut off the circulation. And may they keep your feet warm enough today without getting sweaty by the end of the day. Peace my brother.

I don’t know when I started collecting elks (and moose and reindeers), but I think my first one was a cuddly toy from IKEA. Every year in December I bring them all out for decorating, and they always seem to have multiplied during the year. Since they’re all out and about now, I’ll be taking photos of them to post here. I hope you like them as much as I do and I wish you a merry end-of-the-year festivity, no matter what you call it!

This small (8cm tall) metal elk is, strictly speaking, not mine. I included it in a self-made advent calendar for my wife in 2009. Since then he has always got a nice place to hang near the top of our Christmas tree.

I don’t bother much about distinguishing between elks, moose and reindeers, so this red felt reindeer is an “elk”, as far as I’m concerned. In some years we hang him in a window, in others he hangs on a wall. The green star in this photo was a gift from our friend Susan, and it’s also part of our annual Christmas decoration.

A man walks along a shore and finds a bottle. He opens it and out comes a strange being who says “Thank you ever so much, dear fisherman, for freeing me. I am a genie, and I’ve been locked up for centuries. As a sign of my gratitude, I offer you a wish. What would you like?”

“Thanks yourself,” says the man. “BTW, I’m not a fisher, but a professor of mathematical logic. And I’ve heard this story before. Some idiots ask for a million dollars or happiness or something similar. But I’ve dreamed of this moment for years and planned ahead. My wish is: I want you to grant me ten wishes.”

“Smartarse, eh?” says the genie. “We were warned about your kind in genie training. What you want isn’t a wish, but a ‘meta wish’, a wish about wishes. And that you can’t have. You must choose something material, like a ton of gold or a pink unicorn, or something immaterial, like intelligence or eternal life. If what you wish for doesn’t exist yet, I can create it for you. But meta wishes are out.”

“Okay,” replies the mathematician, “then I want ten bottles with genies like you inside.”

I have a number of mathematical puzzles about a (ficticious) French friend of mine called Nepomuk. Here’s the first of a series:

Nepomuk is driving to Paris, and he passes a road sign telling him the distance left. Unluckily, he’s a bit short-sighted, and so all he sees on the sign is that the number of miles to Paris has three digits, with the middle one being a zero:

Nepomuk travels along at a constant speed, and after exactly one hour he passes a road sign telling him that he’s still YX miles from Paris — the same two digits appear, but inverted.

And yet another hour later (he’s still driving at the same constant speed), he sees a sign telling him that he’s only XY miles from Paris — the same digits as on the first sign, but without the zero.

The mayor of a Greek town visited a town in Italy and was invited to dinner at the Italian mayor’s home. The Greek marveled at the splendour in which his colleague lived — a large house with a nice garden, both well tended, and so he asked “Dear colleague, how can you afford all this luxury on what must be quite a modest salary?”

The Italian took him to the window and said “Do you see that bridge over there? The EU gave us enough money to build a two-lane construction, but we made it single-lane, installing a set of traffic lights instead to prevent cars from driving over it from both ends at the same time. What we saved went into this house.”

The year after that, the Italian went to Greece to visit his new friend. He found his colleague living in a huge villa, surrounded by a park, with a large garage full of sports cars. At dinner, the Italian asked “How on earth did you get this much on your salary, which must be even less than mine?”

The Greek took him to the window and said “Do you see that bridge over there?”

An “elliptical trainer” is an exercise machine, intended to give its user the same physical experience that he could get from climbing up stairs or just going for a walk. Here’s my “artist’s impression” of one of these things:

The basic idea is that the athlete (blue in this picture) steps up and down on two boards (only one shown here) which are attached to a wheel behind him (that can be slowed down with a brake to make him exert himself more) and to vertical bars that he holds on to, which swivel fore and back around a pivot marked “T” in this sketch.

All this time, the athlete’s foot remains on a spot “F” on the moving board, and apparently this point F moves along an elliptical curve (green in the sketch above) — hence the name of this machine.

This contraption was recently the subject of a limerick in the OEDILF, and in a private discussion with my fellow OEDILF author PGS (Holger Martin), the question arose whether the green curve in this sketch really is an ellipse, or only an egg-shaped non-circular shape. In other words: is the elliptical trainer really “elliptical”?

Obviously, this is just a simple question about planar geometry involving a circle, a circular arc and some straight lines, so I thought I’d be able to determine the green shape quite easily. It’s turned out to be a real pest though. I hope I can get it worked out later this week.